Throwing off LE isn't the main reason he took it, in my mind.
He took it either because he forgot he had it, or because he felt it might have his DNA and is the phone isn't all that flammable, or because he knew that once turned off, it was not an immediate risk for him to have it. But if this last circumstance were true, I think he would have shut it off at the CS. So I lean toward the other two scenarios.
As far as why she might drive to a different store, I know that for me, when I go out to get a coffee, sometimes it's not just about getting the coffee. It's about making an excuse for myself to leave the house and wander a bit. Maybe she just felt like going for a drive, or changing it up, if she had been to that store too many times lately.
On the tree cover, surely a summer test will be more representative, but I am not speaking from a perspective of no experience on this. I do a lot of metal detecting in the deep woods. I use old maps from the 17 & 1800s to locate old house sites that are no longer there. On my phone, I use a similar program to plot the old sites on a map before I go. Then head out, and I use my phone's GPS to locate the pre-plotted locations. This summer I did this for a week with a friend in Vermont. We hiked blindly, sometimes miles into the woods toward the dot I placed on the map. When we reached the spot, there was the old foundation, right where It should have been. These areas were significantly more remote than Princeton. What I am trying to say is that although there may at times be glitches and inaccuracies, I think we need to put a little more faith in the technology aspect of the case. I have very strong reason to believe that the phone was near mountain barn at 2:25pm.
That's fine, It's ok that we can disagree. Forgetting he had it on him means that he had it in his pocket. I know you used the example that if you want to take something away from a baby, you keep it on you. You are assuming that the baby is still free to walk around, and as we know, that doesn't apply here. My thought is that he took her phone, and threw it as far as he could. If he was on top of her, all she would have had to do is go for the phone, if it was in his back pocket, Not saying she would have got it, But, I do know that if he threw it, she wouldn't have. And then there's the thought of the cover up, and my thought is that if he spent time building a fire, he would have made sure that phone was not on him. You mentioned in another post that many here think he was tech savoy. I must have missed those posts because this is the first time I have seen that, but, if he was in your words, then again, why take it knowing he would be a target.
I have to also disagree with burning the phone.If he thought a fire would destroy DNA on her body ,I would think the same applied with the phone ,and I'd be willing to bet he could have succeeded with doing that with the phone much easier.That phone would be charred.
I know what you mean about the ride to the store. The reason I asked, is we agree that LE sat the family down, and because of the details that " LE believes she went to the store for a drink around noon, and we know they took the tapes and more likely than not never told anyone at the Mountainside the results of the review, I'm not so sure I'd dismiss that she did go based on an employees thought only. Even tone of voice can be deceiving. He may swear that nobody did see her, and I know you said there were only two people in front of you, at the counter, so it wasn't that busy at about the same time of day, Think Sundays may be a little more busy?
I believe you have experience with the GPS on your phone. I can also say, that although I wasn't clear how the "FindMyPhone" app worked, I too have a little experience with GPS. As a Pilot, I have studied GPS systems. The FAA has what is called a WAAS System, developed specially for aircraft, and the reason is because the standard GPS system is not reliable. Although you have never had a non accurate signal, and in your experiment your system was accurate updating every minute and a half, WAAS is required to update every 5 seconds or less. It is a complete different system than the one you know, and it relies on ground stations and a separate satellite system all together. The reason, Because GPS is not always reliable, and that system corrects the inaccuracies. You won't find an FAA approved GPS system in a $600.00 Phone, because the GPS alone starts at about $14,000, and if you want a decent stack, plan on spending $35,000. So although I do have faith in technology, the GPS in a phone is not always reliable.
Google "why is the location of my phone wrong." There are 7 pages of tech support just on that subject alone," so I think it's fair to say it's not all that uncommon of a problem.
If you want to use that in building a theory, great, however I think it's premature to state it as fact, as long as there is no tree coverage. JMO.